The hydrogen spillover mechanism has been discussed in the field of hydrogen storage and is believed to have particular advantage over the storage as metal or chemical hydrides. We investigate conditions for practicality realizing the hydrogen spillover mechanism onto carbon surfaces, using first-principles methods. Our results show that contrary to common belief, types of hydrogenation configurations of graphene (the aggregated all-paired configurations) can satisfy the thermodynamic requirement for room-temperature hydrogen storage. However, the peculiarity of the paired adsorption modes gives rise to a large kinetic barrier against hydrogen migration and desorption. It means that an extremely high pressure is required to induce the migration-derived hydrogenation. However, if mobile catalytic particles are present inside the graphitic interstitials, hydrogen migration channels can open and the spillover phenomena can be realized. We suggest a molecular model for such a mobile catalyst which can exchange hydrogen atoms with the wall of graphene.